Copyright © 2010 Aviad Roitgrund and Lawrence Horwitz. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We review the formulation of the problem of electromagnetic self-interaction of a relativistic charged particle in the framework of the manifestly covariant classical mechanics of Stueckeleberg, Horwitz, and Piron. The gauge fields of this theory, in general, cause the mass of the particle to change. We study the four dynamical off-mass-shell orbit equations which result from the expansion of Green's function in the Lorentz force equation for the self-interaction. It appears that there is an attractor in this system which stabilizes the motion of the
relativistic charged electron. The attractor may acquire fractal characteristics in the presence of an external field and thus become a strange